Oil Saturation Delimiting Method with Jointly Processing of Nuclear Magnetic Resonant Response (nmr) Data of Oil and Rock Samples in in Natura Condition

The present invention is part of the technical field of oil and gas, specifically related to modeling, simulation and evaluation of oil reservoirs, and refers to a method for delimiting oil saturation (S) with the jointly processing of data from the nuclear magnetic resonant (NMR) response of oil and rock samples in in natura condition.

The identification and quantification of the fluid contents of a geological formation based on data collected in situ is a difficult and complex activity, especially when it comes to classifying the volumes of water and hydrocarbons in an oil reservoir. Typically, decisions in the context of exploration and production of these deposits are supported by measurements made by tools run along the drilled wells (log).

These measurements are commonly restricted to physical amounts that are not of direct interest but are used to infer properties and characteristics of real interest of the geological formation, such as its porosity, hydrocarbon saturation (oil or gas) and its permeability. Log data are often, or need to be, supplemented by another set of measurements of the same physical amounts, acquired, however, under the more rigorous and precise experimental context of laboratories.

To make this possible, physical sampling of rock samples and formation fluids is used at specific intervals in the well. These samples are then conditioned according to the purpose of their analysis or their nature and sent to the competent laboratories.

Among the physical processes tested both in the log and laboratory context, the NMR response of the fluids of a formation stands out as one of the most relevant data for the identification, classification and quantification of its content. An NMR test, in any experimental context, is capable of separating and measuring the magnetization of the atomic nuclei present only in the fluids of a formation when it is subjected to magnetic fields.

In particular, the dynamics of the magnetization of hydrogen nuclei (spin nuclear) present in the water molecules of the formation brine and in the hydrocarbon molecules are observed. The equilibrium nuclear magnetization of each fluid is proportional to its mass and, for this reason, the observation of the total nuclear magnetization provides an indirect way of determining the porosity of the formation (since the fluids present in a geological stratum can only occupy the interstices of its rocks).

On the other hand, separating from this observation the contribution relative to each type of fluid is particularly difficult, because NMR is a technique sensitive to the nuclear spins of all fluids collectively; the acquisition of the NMR response isolated from them cannot be commonly performed on rock samples. This aspect of NMR data acquisition makes its analysis particularly difficult with regard to identifying and quantifying the contribution of each fluid, thus making it difficult to use the NMR response as a procedure for estimating fluid saturations, although, as already stated, the techniques involved are quite sensitive to these amounts.

A widely used strategy for this purpose consists of observing the entire NMR response of the system. Instead of limiting oneself to the magnitude of the NMR signal, from which the equilibrium nuclear magnetization is extracted, the entire evolution of the response is monitored from its activation to its cessation, that is, the entire development of the polarization, or the complete decay of the nuclear magnetization, depending on the experimental protocol.

Nuclear spins exhibit a precession movement around the axis defined by the applied static magnetic field. Under a given static field magnitude, B, the frequency of this movement is an identifying attribute of the nuclear species, called the Larmor frequency, ω. The application of a static field forces the nuclear spins, which are essentially magnetic dipoles, to align with the applied field. This process establishes the nuclear magnetization and has a characteristic time, denoted by T, roughly speaking, associated with each molecular species that harbors spins of the probed nuclear species.

Thus, the nuclear magnetic moment of hydrogens residing in water molecules has a polarization time (or longitudinal relaxation) that is different from the nuclear magnetic moment of hydrogens associated with a given chemical component of petroleum, such as paraffins. In this way, each molecular class present in the fluids of a formation can be associated with a nuclear magnetization and distinguished by its characteristic polarization time. This principle is summarized in the model equation:

This time is denoted here as t→? in agreement with the limit of Equation (1) and the final or equilibrium magnetization of the spins by M.demonstrates the development of an NMR polarization in a rock sample, in which one can clearly identify the stabilization of the acquired signal at a level that determines the Min arbitrary units (u.a.) in the test in question.

Although a classification of the fluids contained in a geological formation can, in theory, be made based on an inversion of the NMR response of the system, in practice, such a procedure encounters some difficulties. The inversion problem consists of determining the unknowns {m} and {T} from a finite set of observations of the response M(t) at specific instants.

An obvious difficulty is that, even in a perfect inversion, distinct molecules may present similar relaxation times and it is not known, a priori, whether such a coincidence in fact introduces imprecision into the analysis process. Furthermore, it is impossible to distinguish with absolute certainty the molecular species in these situations, since the relaxation times are natural indexes only of the relaxometric classes. Other difficulties present reside (1) in the non-linearity of the relaxation times, T, with the system response, (2) in the coupling of these parameters with the magnetizations m, and (3) in the typical lack of knowledge of the number of relaxometric species present in the system (the number of indexes i).

All these issues, however, are resolved by replacing the discrete model of Equation (1) with the continuous model:

More technically, neither the acquisition of the NMR response of the system, nor the spectrum of relaxation times associated with it are continuous objects; in any test, the detection of the signal is only performed over a discrete and finite set of observation times, {t}, and the spectrum is more easily conceived and effectively computed over a partitioning of the admissible band of relaxation times into sub-bands. The model of Equation (2) thus discretized is described by

An inversion of Equation (3), on the other hand, is a difficult task, largely because the kernel of the discretized problem, K, is often a non-invertible matrix, which means that there is more than one object m compatible with the observation M. Therefore, the particular choice of a viable object as the spectrum of the system requires more information about the latter than is contemplated in the experimental observation and depends specifically on the methodology with which this additional information is used to mark such an object as the unique solution of Equation (3) that also satisfies all the a priori knowledge (observation-independent) available about the spectrum.

The non-negativity condition, m≥0 for all j (represented compactly as m≥0), is an example of this type of complementary information commonly used in the inversion methods pertinent to the problem in question.

In addition to this issue of non-uniqueness, inverse problems such as the one presented also suffer from an issue regarding the non-existence of solutions, often attributed to acquisition noise or other deviations from the real response of the system, such as modeling errors or errors arising from the discretization of the model. It is then established that the acquired data is related to the ideal observation of the system according to:

It is not uncommon for there to be situations wherein the noise level exceeds the intensity of the system response over a range of observations relevant to the problem, which results in obtaining data that is less supported or adequate for the assumed model and consequently in an inconsistent inversion, when Mis taken indiscriminately as a good approximation for M.

Finally, although the problem was motivated by the observation of the development of nuclear polarization (longitudinal relaxation), the explanation extends to the analysis of several other NMR response tests by redefining the kernel, such as:

There are several ways in which the imprecision of measurements can be considered in the inversion method so that the solutions found are consistent and compatible with the degree of fidelity of the observations to the ideal response of the system. Specifically for the class of conditioned linear inverse problems to which the inversion of Equation (3) belongs, the best-established methodology is the regularized minimization of the mean square of the residuals (MSR):

Inference methods comprise another paradigm that enjoys popularity. Entropy Maximization (MaxEnt) is a fundamental axiom of Information Theory, which assumes that the distribution (spectrum) that best meets the set of imposed restrictions (observation, non-negativity, normalization) is obtained without introducing unjustified biases. A classic MaxEnt formulation consists of the program:

In addition to the difficulties inherent in the inversion of the NMR response, the classification of the discrete spectrum entries, m, into components specifically associated with one or another fluid is frustrated due to a mechanism of differentiation and shortening of relaxation times, which is quite relevant for water molecules in the regions of the porous volume where the fluid adheres to the surfaces of the mineral framework of the rocks.

The process is known as surface relaxivity, is induced by the presence of paramagnetic impurities housed in the solid interface of the matrix and overcomes the material (or intrinsic) relaxation of a molecular class when, simultaneously, the molecules (1) are polar (i.e., they have an electric dipole), (2) have high mobility within the fluid phase wherein they are inserted (effective molecular transport), and (3) can come into contact with the pore surface and remain confined to relatively narrow regions of the pore volume (such as small pores, surface coating films, menisci or small pockets of fluid adhered to the interface).

The first two conditions are more relevant in the water molecules of the brine of the formation than in the molecules present in oil, whose typical constitution is predominantly marked by nonpolar and low mobility molecules. The third situation is determined by the preferential wettability of the formation, consequently, it can be valid for molecules of all fluids to some degree.

As stated, the three conditions must be valid for a considerable dispersion of relaxation times of the same molecular class to be observed. A simplification, fundamental to the present invention, therefore, is that only water molecules are sensitive to the surface relaxivity mechanism and, therefore, any NMR response related to hydrocarbons retains its intrinsic characteristics. This hypothesis allows the response of petroleum to be distinguished from that of the rest of the formation in situations where a sample of the fluid is accessible for an isolated observation of its signature, as shown in.

In the laboratory context, this is often possible either by extracting a small volume of fluid directly from the rock sample or by using a fluid sample originally collected in situ for chemical analysis or tracing purposes. The NMR response of oil in a geological formation varies little with collection depth, which allows the same fluid sample to be used in the analysis of several rock samples from the same well.

Knowledge of the NMR response of hydrocarbons in the formation allows this information to be highlighted in Equation (1), and the oil saturation level, S, and, complementarily, the saturation of all other fluids, S, (no denotes non-oil) to be introduced directly into the modeling. In terms of observations, there is

An entry mof the spectrum of a sample quantifies the number of nuclear spins that present relaxation times within the range [T, T]; in this way, the entire spectrum can be normalized by the number of spins of the sample (equilibrium nuclear magnetization) so that each entry of the normalized spectrum, x, denotes the frequency or relative abundance with which spins relaxing in the corresponding range (relaxometric class) are observed in the sample. That is, it is defined:

From the perspective of Equation (2) and by the definition of the discrete spectrum, Equation (5), the property is directly deduced from the equation above:

It is clear that the normalization of the spectrum can be performed on each of the response phases of the sample, therefore,

An important reinterpretation of Equation (13), motivated by the relationship above, is that, in the case of multi-component systems, such as geological formations, xconsists of the relative abundance in the class j of spins on all components of the system, that is,

For example, the relative abundance of each component, xα (Sor So in the particular problem), is defined by: